The probabilistic method is a nonconstructive method, primarily used in combinatorics, was pioneered by Paul Erdös, for proving the existence of a prescribed kinds of mathematical objects. Suppose we want to show that an object of a specific class with a certain property exists. Often it might be difficult to show the existence by explicitly constructing such an object. In the light of this dif...

One of the purposes of consciousness is to acquire knowledge. The models of this task traditionally assume a division between the known and the knower, a division that leads into doubtful reasoning about some kind of (frequently disguised) homunculus. The current paper tries to avoid such fallacies by viewing the adaptation of the mind as an evolutionary process, a process distinct (but not ind...

In the simulation of flows, the correct treatment of the pressure variable is the key to stable time-integration schemes. This paper contributes a new approach based on the theory of differential-algebraic equations. Motivated by the index reduction technique of minimal extension, a decomposition of finite element spaces is proposed that ensures stable and accurate approximations. The presented...

in the 1960's noboru iwahori and hideya matsumoto, eiichi abe and kazuo suzuki, and michael stein discovered that chevalley groups $g=g(phi,r)$ over a semilocal ring admit remarkable gauss decomposition $g=tuu^-u$, where $t=t(phi,r)$ is a split maximal torus, whereas $u=u(phi,r)$ and $u^-=u^-(phi,r)$ are unipotent radicals of two opposite borel subgroups $b=b(phi,r)$ and $b^-=b^-(phi,r)$ contai...

Among different discretization approaches, Finite Difference Method (FDM) is widely used for acoustic and elastic full-wave form modeling. An inevitable deficit of the technique, however, is its sever requirement to computational resources. A promising solution is parallelization, where the problem is broken into several segments, and the calculations are distributed over different processors. ...

One of the fundamental challenges in designing distributed object applications (DOAs) is application partitioning. Partitioning is a technique through which all the necessary partitions or components of the application, particularly distributable ones, are discovered. This research proposes a technique to help designers in partitioning DOAs such that a justifiable application structure is achie...